can falling commet be used in an non-combat open showdown, am i able to target akali silent since she's entered the battlefield but i'm not there but i send my spell?

You can play Falling Comet during the non-combat Showdown's Open State — but you can't target Akali, Silent with it.

Falling Comet has [Action], so it's playable in Showdown Open states (Rule 159.2.a.1), and targeting a battlefield you have no unit at is fine — there's no restriction on targeting other locations during a Showdown (FAQ #1429/#6777). The problem is Akali herself: her passive makes her untargetable by enemy spells and abilities unless she's in combat. A Non-Combat Showdown never initiates combat or assigns Attacker/Defender designations (Rule 464.2.c.3), so she's not "in combat" during it — meaning Falling Comet can't legally choose her at all (Rule 758, FAQ #11754). If she were in a Combat Showdown instead, she'd be a perfectly legal target.